590198 ÷ 45 
Our goal is to divide 590198 by 45.

Step 1:
When dividing 5 by 45, we get 0 with a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 5 after subtracting 0 from 5.
Fetch the next digit (9) from the dividend, attach it to 5 and continue: 59 / 45

Let's proceed to step 2:
The number 45 fits into 59 1 times, leaving a remainder of 14.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
If we take 45 away from 59, we end up with 14.
Include the next digit (0) from the dividend after 14, then repeat: 140 / 45

Let's proceed to step 3:
When dividing 140 by 45, we get 3 with a remainder of 5.
Record the quotient 3 as the next digit in the result. 
Result so far: 13.0
Subtracting 135 from 140 leaves us with 5.
Take the next digit (1) from the dividend and append it to 5, then repeat: 51 / 45

Advancing to step 4:
When dividing 51 by 45, we get 1 with a remainder of 6.
Use 1 as the next digit of our solution. 
Result so far: 131.0
Deduct 45 from 51 and we're left with 6.
Grab the next digit (9) from the dividend, add it to 6, then carry on: 69 / 45

Let's proceed to step 5:
If we divide 69 by 45, we get 1 and a remainder of 24.
The next digit of our result is 1. 
Result so far: 1311.0
Subtracting 45 from 69 leaves us with 24.
Fetch the next digit (8) from the dividend, attach it to 24 and continue: 248 / 45

Let's proceed to step 6:
The number 45 fits into 248 5 times, leaving a remainder of 23.
Record the quotient 5 as the next digit in the result. 
Result so far: 13115.0
Subtracting 225 from 248 leaves us with 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Step 7:
45 can be fit into 230 5 times, resulting in a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 13115.5
The remainder is 5 after subtracting 225 from 230.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

On to step 8:
When dividing 50 by 45, we get 1 with a remainder of 5.
Put 1 as the next digit of the answer. 
Result so far: 13115.51
If we subtract 45 from 50, we get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Moving on to step 9:
If we divide 50 by 45, we get 1 and a remainder of 5.
The number 1 becomes the next digit in our result. 
Result so far: 13115.511
Deduct 45 from 50 and we're left with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

After the division, we end up with 13115.511 and a remainder of 0.0005.